When you import food to juice population growth, there's a lag of a x number of days before the population reaches the new daily food allotment.

Is there a similar lag for transitioning new population from consumption-only to food producers? In other words, in a settlement with good farmland and a recent population boom, how long does it take before a new peasant (created by new food) is creating just as much food as other peasants? Or is it instant?

I keep having a problem where I dump food into a settlement to boost the population, but when I cutoff the imported food, the population falls off because the new peasants don't produce enough food to sustain themselves.

So, I think there's a misconception here. Settlements naturally produce whatever food they are able to. A few buildings boost this based on what they do in real life, things like the mill, the market, etc. But a settlement will always produce as much food as it can efficiently, and a settlement will always try to get to as many settlers as that food supply can sustain.

So, when you import food, you're not getting more people that produce the same amount of food. Your getting more people that each bring down the individual amount of food produced. The total amount may keep going up for a while, but eventually, adding more people will NOT increase food production enough to be noticed.

This is to simulate the usage of arable land in a region. There's a point where even adding more farmers for all the arable land in the region does not actually produce more food, because all that land is already being farmed as efficiently as possible.

Oh okay. I thought there was a one-to-one relationship of food to peasant. And this figure is unique to each settlement? Or do two settlements of equal square mileage and identical land type have the same base amount of food production?

Each additional farmer grows a little less food than the one before. The very first peasant grows quite a bit of food, but it declines per-peasant, so at some point you have a peasant eating 1 food and growing 1 food, but you still have an excess of food at that point because all the previous peasants created a surplus. So after the "break even" point, the surplus is eaten away quicker and quicker per peasant (however never more than 1 per peasant). However this isn't all bad because each peasant also produces other types of resources.

Also, when you transfer food it will have an inflated effect. e.g. 50 food feeds another 50 peasants, and those 50 peasants might grow 25 food, feeding another 25 peasants, who then grow 10 food, etc etc. So you might get an additional 80 peasants in your new town, instead of just 50. However it will have the exact opposite effect in the original town since 50 peasant are no longer fed and they now lose the additional food production of those 50 guys, which has further knock-on effects. The takeaway message is not to transfer too much food at once.(because the original town could drop to a too-low level to sustain all your buildings).